Vector Dot (Inner) Product Calculator

An online calculator for finding the dot (inner) product of two vectors, with steps shown.

$$$\langle$$$ $$$\rangle$$$
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$$$\langle$$$ $$$\rangle$$$
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Your Input

Calculate $$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle$$$.

Solution

The dot product is given by $$$\mathbf{\vec{u}}\cdot \mathbf{\vec{v}} = \sum_{i=1}^{n} u_{i} v_{i}$$$.

Thus, what we need to do is multiply the corresponding coordinates and then add up the results: $$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle = \left(7\right)\cdot \left(1\right) + \left(0\right)\cdot \left(-1\right) + \left(-2\right)\cdot \left(4\right) = -1.$$$

Answer

$$$\left\langle 7, 0, -2\right\rangle\cdot \left\langle 1, -1, 4\right\rangle = -1$$$A